What your code is doing is reading the file line by line into the variable
'MyString', each line replacing the previous one. At the end you write the
contents of 'MyString', then containing the last line as you have seen, to
your bookmark.

You could shift the moving text to your document inside the loop and
continue line by line but you would need to alter it slightly to work
properly with the bookmark, or ...

... you could do the whole thing more easily with ...

   ActiveDocument.Bookmarks("Test").Range.InsertFile
FileName:="C:\files\test.txt", Link:=False

--
Enjoy,
Tony

If you want to do it this way, you have to collect the lines as they're read
from the file and append them to a string:

   Dim tempString, MyString
   Open "C:\files\test.txt" For Input As #1
   Do While Not EOF(1)
       Input #1, tempString
       MyString = MyString & tempString & vbCr
   Loop
   Close #1
   ' remove last vbCr
   MyString = Left(MyString, Len(MyString) - 1)

   ActiveDocument.Bookmarks("Test").Range.Text = MyString

But you can do the whole thing in one step with the InsertFile command:

   ActiveDocument.Bookmarks("Test").Range.InsertFile _
       FileName:="c:\files\test.txt"